A Note On The Expansion Coefficient Of Geometrical Optics

Author : Morris Kline
Publisher : Unknown
Page : 1 pages
File Size : 50,8 Mb
Release : 1961
Category : Geometrical optics
ISBN : OCLC:227264627

Get Book

A Note on the Expansion Coefficient of Geometrical Optics by Morris Kline Pdf

The expansion coefficient of geometrical optics is a measure of the cross section os, New York U., N.Y.A NOTE ON THE EXPANSION COEFFICIENT OF GEOMETRICAL OPTICS, by Morris Kline. 1961, 12p. (Research rept. no. EM-166) (Contract AF 19(604)5238) Unclassified report DESCRIPTORS: *Optics, *Electromagnetic theory, *Differential geometry, Light, Electron optics, Series, Geometry. The expansion coefficient of geometrical optics is a measure of the cross section of a tube of rays and has the physical significance of measuring the intensity of the light propagating along the tube. Strictly, it is a point concept and measures the intensity along an individual ray. This paper presents a convenient expression for the expansion coefficient. The mathematics involved is merely an application of known differential geometry but the expression derived seems to be new and is apparently unknown to workers in electromagnetic theory. The new feature of this paper is that the formula given for the variation of the expansion coefficient holds in inhomogeneous isotropic media and reduces immediately to the widely known expression for the expansion coefficient in homogeneous media, which involves the Gauss curvature of the wave front. (Author).

Author : Morris Kline
Publisher : Forgotten Books
Page : 28 pages
File Size : 47,6 Mb
Release : 2017-12
Category : Electronic
ISBN : 026076518X

Get Book

A Note on the Expansion Coefficient of Geometrical Optics (Classic Reprint) by Morris Kline Pdf

Excerpt from A Note on the Expansion Coefficient of Geometrical Optics The objective of this paper is to derive a useful form for the function K as a function of s, s being arc length along a ray. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Author : Morris Kline
Publisher : Forgotten Books
Page : 26 pages
File Size : 52,6 Mb
Release : 2015-06-25
Category : Reference
ISBN : 1330162722

Get Book

A Note on the Expansion Coefficient of Geometrical Optics by Morris Kline Pdf

Excerpt from A Note on the Expansion Coefficient of Geometrical Optics A Note on the Expansion Coefficient of Geometrical Optics was written by Morris Kline. This is a 28 page book, containing 7763 words and 3 pictures. Search Inside is enabled for this title. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Author : Anonim
Publisher : Unknown
Page : 1216 pages
File Size : 50,6 Mb
Release : 1961
Category : Science
ISBN : OSU:32435022153605

Get Book

U.S. Government Research Reports by Anonim Pdf

Author : Defense Documentation Center (U.S.)
Publisher : Unknown
Page : 1766 pages
File Size : 48,7 Mb
Release : 1961-07
Category : Technology
ISBN : UTEXAS:059172131213032

Get Book

Technical Abstract Bulletin by Defense Documentation Center (U.S.) Pdf

Author : Mireille Levy
Publisher : IET
Page : 360 pages
File Size : 42,5 Mb
Release : 2000
Category : Mathematics
ISBN : 0852967640

Get Book

Parabolic Equation Methods for Electromagnetic Wave Propagation by Mireille Levy Pdf

Provides scientists and engineers with a tool for accurate assessment of diffraction and ducting on radio and radar systems. The author gives the mathematical background to parabolic equations modeling and describes simple parabolic equation algorithms before progressing to more advanced topics such as domain truncation, the treatment of impedance boundaries, and the implementation of very fast hybrid methods combining ray-tracing and parabolic equation techniques. The last three chapters are devoted to scattering problems, with application to propagation in urban environments and to radar-cross- section computation. Annotation copyrighted by Book News, Inc., Portland, OR

Author : Virendra N. Mahajan
Publisher : SPIE Press
Page : 476 pages
File Size : 51,5 Mb
Release : 1998
Category : Science
ISBN : 081942515X

Get Book

Optical Imaging and Aberrations: Ray geometrical optics by Virendra N. Mahajan Pdf

Based on the author's lectures at the University of Southern California, where he teaches a graduate course in optical imaging and aberrations, this volume provides an understanding of how aberrations arise in optical systems and how they affect imaging. Emphasis is placed on the primary aberrations of simple optical systems as a foundation for the design of more complex and high image-quality systems. Each chapter ends with a set of problems. A separate volume (Volume 2) treats imaging based on diffraction. Annotation copyrighted by Book News, Inc., Portland, OR

Author : Mark H. Holmes
Publisher : Springer Science & Business Media
Page : 447 pages
File Size : 41,9 Mb
Release : 2012-12-05
Category : Mathematics
ISBN : 9781461454779

Get Book

Introduction to Perturbation Methods by Mark H. Holmes Pdf

This introductory graduate text is based on a graduate course the author has taught repeatedly over the last ten years to students in applied mathematics, engineering sciences, and physics. Each chapter begins with an introductory development involving ordinary differential equations, and goes on to cover such traditional topics as boundary layers and multiple scales. However, it also contains material arising from current research interest, including homogenisation, slender body theory, symbolic computing, and discrete equations. Many of the excellent exercises are derived from problems of up-to-date research and are drawn from a wide range of application areas. One hundred new pages added including new material on transcedentally small terms, Kummer's function, weakly coupled oscillators and wave interactions.

Author : Anonim
Publisher : Unknown
Page : 788 pages
File Size : 48,7 Mb
Release : 2024-06-30
Category : Aeronautics
ISBN : STANFORD:36105211293415

Get Book

OAR Cumulative Index of Research Results by Anonim Pdf

Author : United States. Air Force. Office of Aerospace Research
Publisher : Unknown
Page : 800 pages
File Size : 53,7 Mb
Release : 1959
Category : Aeronautics, Military
ISBN : CORNELL:31924057100251

Get Book

OAR Quarterly Index of Current Research Results by United States. Air Force. Office of Aerospace Research Pdf

Author : David S. Loshin
Publisher : Elsevier Health Sciences
Page : 202 pages
File Size : 48,6 Mb
Release : 2015-01-28
Category : Science
ISBN : 9781483293653

Get Book

The Geometrical Optics Workbook by David S. Loshin Pdf

This workbook is designed to supplement optics textbooks and covers all the traditional topics of geometrical optics. Terms, equations, definitions, and concepts are discussed briefly and explained through a series of problems that are worked out in a step-by-step manner which simplifies the problem-solving process. Additional practice problems are provided at the end of each chapter. * - An indispensable tool when studying for the state and National Boards * - An ideal supplement to optics textbooks * - Covers the traditional topics of geometrical optics.

Author : Milton Katz
Publisher : World Scientific
Page : 332 pages
File Size : 49,7 Mb
Release : 2002
Category : Science
ISBN : 9812382240

Get Book

Introduction to Geometrical Optics by Milton Katz Pdf

This book is the culmination of twenty-five years of teaching Geometrical Optics. The volume is organised such that the single spherical refracting surface is the basic optical element. Spherical mirrors are treated as special cases of refraction, with the same applicable equations. Thin lens equations follow as combinations of spherical refracting surfaces while the cardinal points of the thick lens make it equivalent to a thin lens. Ultimately, one set of vergence equations are applicable to all these elements.The chapters are devoted to in-depth treatments of stops, pupils and ports; magnifiers, microscopes, telescopes, and camera lenses; ophthalmic instruments; resolving power and MTF; trigonometric ray tracing; and chromatic and monochromatic aberrations. There are over 100 worked examples, 400 homework problems and 400 illustrations.First published in 1994 by Penumbra Publishing Co.

Author : Anonim
Publisher : Unknown
Page : 1368 pages
File Size : 55,6 Mb
Release : 1966
Category : Research
ISBN : STANFORD:36105013139196

Get Book

Bibliography of Scientific and Industrial Reports by Anonim Pdf

Author : Jean-François Coulombel,Mark Williams
Publisher : American Mathematical Soc.
Page : 143 pages
File Size : 52,7 Mb
Release : 2020-04-03
Category : Education
ISBN : 9781470440374

Get Book

Geometric Optics for Surface Waves in Nonlinear Elasticity by Jean-François Coulombel,Mark Williams Pdf

This work is devoted to the analysis of high frequency solutions to the equations of nonlinear elasticity in a half-space. The authors consider surface waves (or more precisely, Rayleigh waves) arising in the general class of isotropic hyperelastic models, which includes in particular the Saint Venant-Kirchhoff system. Work has been done by a number of authors since the 1980s on the formulation and well-posedness of a nonlinear evolution equation whose (exact) solution gives the leading term of an approximate Rayleigh wave solution to the underlying elasticity equations. This evolution equation, which is referred to as “the amplitude equation”, is an integrodifferential equation of nonlocal Burgers type. The authors begin by reviewing and providing some extensions of the theory of the amplitude equation. The remainder of the paper is devoted to a rigorous proof in 2D that exact, highly oscillatory, Rayleigh wave solutions uε to the nonlinear elasticity equations exist on a fixed time interval independent of the wavelength ε, and that the approximate Rayleigh wave solution provided by the analysis of the amplitude equation is indeed close in a precise sense to uε on a time interval independent of ε. This paper focuses mainly on the case of Rayleigh waves that are pulses, which have profiles with continuous Fourier spectrum, but the authors' method applies equally well to the case of wavetrains, whose Fourier spectrum is discrete.

Author : A A Fuki,Yu A Kravtsov,O N Naida
Publisher : CRC Press
Page : 200 pages
File Size : 48,8 Mb
Release : 1998-02-25
Category : Science
ISBN : 9056990365

Get Book

Geometrical Optics of Weakly Anisotropic Media by A A Fuki,Yu A Kravtsov,O N Naida Pdf

This book explores recent developments in QIA and describes the application of the theory to different branches of wave physics, from plasma physics, quantum physics, and ionospheric radio wave propagation to acoustics, optics, and astrophysics. This is an up-to-the-minute exposition of the latest developments in an important new area, written by authors of outstanding reputation. A rich source of both theoretical methods and practical applications, it covers a wide range of problems of general physical significance. Until recently, there was no effective method for describing waves in weakly anisotropic inhomogeneous media. The method of quasi-isotropic approximation (QIA) of geometrical optics was developed to overcome this problem. The QIA approach bridges the gap between geometrical optics of isotropic media (Rytov method) and that of anisotropic media (Courant-Lax approach), thus providing a complete picture of the geometrical optics of inhomogeneous media.